Exact Explicit Solutions of a Nonlinear Evolution Equation

We employ bifurcation method of dynamical systems to investigate exact traveling wave solutions of a nonlinear evolution equation. We obtain some exact explicit expressions of solitary wave solutions and some new exact periodic wave solutions in parameter forms of Jacobian elliptic function. We point out that the solitary waves are limits of the periodic waves in some sense, the results infer that the periodic waves degenerate solitary waves in some conditions.